Exponents Warm UP! For each of the following problems, identify the base and the exponent: 1. 47 2. 1110 3. 1002 ***If a number doesn’t have an exponent, then you can always assume that the exponent is one. For example, 7 = 71

Monomials vs. Polynomials

Monomial A monomial may be… A constant A variable A product of a constant and variable

Polynomial Polynomial- Examples of Polynomials: 6x + 4 15h − 17k2 m3 + 2m2 − 4m + 11

What is an exponent? An exponent is a superscript, or small number written at the top right corner of a number, variable, or set of parentheses

Example 23 Tells you to multiply the base by itself as many times as the exponent says. 2 * 2 * 2 8

-36 Note this negative sign in front of the 3. Because there are no parentheses, you leave the negative sign till the end Write this out

(-3)6 Notice this problem has parentheses with a negative sign on the inside. This time you take the negative into account Write it out

Negatives inside parentheses If the exponent is even, the answer will be positive If the exponent is odd, the answer will be negative.

Laws of Exponents

crcs=cr +s add exponents (5t)(−30t2) (−4a2b)(1ab3) (2x2y)(xz3)(3y2z2)

What do I do with negative exponents? Subtract! (4x3)(x-2) (3y4)(2y-1)

Tic Tac Toe! Decide who will be the x in the group and who will be the o. Choose a problem to simplify. Both you and your partner should solve the problem. If you answered correctly, put your letter on top of the problem. Have your partner choose a problem to solve and repeat the steps above.

Powers raised to powers (23)4 can be written out similar to the way we wrote out exponents in the beginning Now you just need to write the power out the exponent attached to the number each time as well.

Examples

A faster trick You can multiply when you have a power to a power Looks different from the addition case (2x3)(3x4) (2x3)2

(26)2

(104)2

(y3)5

(m3)x

Going one step farther When there is a number or extra variable in the parentheses, you must distribute the power outside the parentheses to both things (4x)2

Another (xy)3

(gm)6

(4w)3

Exponents with Fractions Square the term in the numerator Square the term in the denominator Simplify if possible

Division of exponents  

One catch You may only subtract exponents with the same bases

c4b c2a −4x2y5 2xy3